Answer :
Certainly! Let's solve this problem step-by-step.
We have a cube with a side length of 4 inches and a mass of 5 pounds. We need to find the density of the cube in \(\text{kg/m}^3\).
### Step 1: Convert the side length from inches to meters
First, we convert the side length from inches to millimeters:
[tex]\[ 4 \text{ inches} \times 25 \frac{\text{mm}}{\text{inch}} = 100 \text{ mm} \][/tex]
Next, we convert millimeters to meters by knowing that there are 1,000 millimeters in a meter:
[tex]\[ 100 \text{ mm} \times \frac{1 \text{ m}}{1000 \text{ mm}} = 0.1 \text{ m} \][/tex]
So, the side length of the cube is \(0.1 \text{ meters}\).
### Step 2: Convert the mass from pounds to kilograms
We know that:
[tex]\[ 1 \text{ lb} = 450 \text{ g} \][/tex]
Thus, converting 5 pounds to grams:
[tex]\[ 5 \text{ lbs} \times 450 \frac{\text{g}}{\text{lb}} = 2250 \text{ g} \][/tex]
Next, convert grams to kilograms by noting that there are 1,000 grams in a kilogram:
[tex]\[ 2250 \text{ g} \times \frac{1 \text{ kg}}{1000 \text{ g}} = 2.25 \text{ kg} \][/tex]
So, the mass of the cube is \(2.25 \text{ kilograms}\).
### Step 3: Calculate the volume of the cube in cubic meters
The volume \(V\) of a cube is found using the formula \(V = \text{side}^3\):
[tex]\[ V = (0.1 \text{ m})^3 = 0.001 \text{ m}^3 \][/tex]
### Step 4: Calculate the density in \(\text{kg/m}^3\)
Density \(\rho\) is defined as mass (\(m\)) per unit volume (\(V\)):
[tex]\[ \rho = \frac{m}{V} \][/tex]
Substituting the values we obtained:
[tex]\[ \rho = \frac{2.25 \text{ kg}}{0.001 \text{ m}^3} = 2250 \text{ kg/m}^3 \][/tex]
Therefore, the density of the cube is [tex]\(2250 \text{ kg/m}^3\)[/tex].
We have a cube with a side length of 4 inches and a mass of 5 pounds. We need to find the density of the cube in \(\text{kg/m}^3\).
### Step 1: Convert the side length from inches to meters
First, we convert the side length from inches to millimeters:
[tex]\[ 4 \text{ inches} \times 25 \frac{\text{mm}}{\text{inch}} = 100 \text{ mm} \][/tex]
Next, we convert millimeters to meters by knowing that there are 1,000 millimeters in a meter:
[tex]\[ 100 \text{ mm} \times \frac{1 \text{ m}}{1000 \text{ mm}} = 0.1 \text{ m} \][/tex]
So, the side length of the cube is \(0.1 \text{ meters}\).
### Step 2: Convert the mass from pounds to kilograms
We know that:
[tex]\[ 1 \text{ lb} = 450 \text{ g} \][/tex]
Thus, converting 5 pounds to grams:
[tex]\[ 5 \text{ lbs} \times 450 \frac{\text{g}}{\text{lb}} = 2250 \text{ g} \][/tex]
Next, convert grams to kilograms by noting that there are 1,000 grams in a kilogram:
[tex]\[ 2250 \text{ g} \times \frac{1 \text{ kg}}{1000 \text{ g}} = 2.25 \text{ kg} \][/tex]
So, the mass of the cube is \(2.25 \text{ kilograms}\).
### Step 3: Calculate the volume of the cube in cubic meters
The volume \(V\) of a cube is found using the formula \(V = \text{side}^3\):
[tex]\[ V = (0.1 \text{ m})^3 = 0.001 \text{ m}^3 \][/tex]
### Step 4: Calculate the density in \(\text{kg/m}^3\)
Density \(\rho\) is defined as mass (\(m\)) per unit volume (\(V\)):
[tex]\[ \rho = \frac{m}{V} \][/tex]
Substituting the values we obtained:
[tex]\[ \rho = \frac{2.25 \text{ kg}}{0.001 \text{ m}^3} = 2250 \text{ kg/m}^3 \][/tex]
Therefore, the density of the cube is [tex]\(2250 \text{ kg/m}^3\)[/tex].
